Doppler flow velocity distribution measuring apparatus

ABSTRACT

An apparatus for measuring the velocity distribution in a fluid by a pulse-Doppler method using an ultrasonic waver or an electromagnetic wave. The observation wave is transmitted to and received from the fluid and the reflected echo from the fluid is received so as to obtain the Doppler frequency. A predetermined transverse section is scanned with the observation wave so as to obtain the Doppler velocity distribution in the transverse section. Since the Doppler velocity distribution only contains the component in the direction of the observation wave, the Doppler velocity distribution is cumulatively integrated in the direction orthogonal to the direction of the observation wave and the integrated values are differentiated again in the direction of the observation wave, thereby obtaining the component in the orthogonal direction by calculation. If the observation wave is an ultrasonic beam, it is possible to observe the velocity distribution of the bloodstream in the heart.

Technical Field

The present invention relates to a Doppler flow velocity measuringapparatus and, more particularly, to a Doppler flow velocity measuringapparatus which is capable of obtaining the two-dimensional velocitydistribution of a fluid on a predetermined transverse section by onebeam scanning of said transverse section.

Background Art

A Doppler velocity measuring apparatus for obtaining the flow of a fluidor the movement of a moving member in an object being examined byutilizing a Doppler effect is known. By this apparatus, an ultrasonic orelectromagnetic wave, especially, a pulsating burst wave is transmittedto the object being examined, and a reflected echo is obtained at eachpoint in the direction of the beam so as to utilize a Doppler effect.This method is widely utilized as a pulse-Doppler method.

Such a velocity measurement method is useful for knowing the flowvelocity vector distribution in a predetermined transverse section beingobserved which is composed of a plane or a curved surface by scanningthe transverse section with the transmitted beam. This method is veryuseful for knowing the movement of clouds by using an electromagneticwave, and the bloodstream velocity distribution in the heart of the bodyby using an ultrasonic wave. Especially, in the latter case, it ispossible to observe the bloodstream distribution without invasion andproduce excellent results on the diagnosis of the function of the heartand the like.

As is well known, according to this kind of pulse-Doppler method, sincethe frequency of a received signal deviates depending upon the movementof a reflecting member, the velocity distribution of a fluid along eachpoint of the an ultrasonic beam is obtained from the deviated frequency(Doppler frequency) obtained by comparison between the frequencies ofthe transmitted signal and the received signal. The pulse-Dopplermethod, however, suffers from the serious problem that the velocityinformation obtained from the pulse-Doppler method only provides avelocity component in the direction of a beam.

Therefore, even if two-dimensional velocity distribution information isobtained by moving the pulse beam along a predetermined transversesection by the mechanical movement of a probe or electronic linear orsector scanning, since the information obtained only contains thecomponent in the direction of the beam, the velocity and theacceleration distribution in the displayed image obtained from theinformation and the pressure distribution in the closed region obtainedfrom the velocity information of each pixel contain a large innegligibleerror.

In order to obtain a component in a direction different from thedirection of a beam in the transverse section plane scanned with thebeam, a method of obtaining the correlation of the data in thedirections of adjacent beams is conventionally investigated. However,such calculation of the correlation makes the apparatus complicated andsince the processing speed is lowered, the amount of data observable perunit time is reduced.

The present inventors proposed a method of using an advectiveaccelerating component of a fluid in order to infer the velocitycomponent data in a direction different from the direction of anultrasonic wave, the direction orthogonal thereto in ordinary case, inJapanese Patent Application Nos. 236919/1987 and 236920/1987.

According to the above-described related art, a plurality of burst wavesare transmitted from an ultrasonic probe to a fluid at a predeterminedrecurrence period, the echo obtained from the fluid is received by theultrasonic probe and the flow velocity component data (hereinunderreferred to as "Doppler velocity") at each point in the direction of thebeam is obtained from the received signal every moment by utilizing theabove-described Doppler effect.

The Doppler velocities obtained are sequentially stored in a memory, andthe points which satisfy the conditions for obtaining the advectiveacceleration component are obtained from the thus-stored two-dimensionalinformation. At the points which satisfy the conditions, the advectiveacceleration component is calculated and at the other points, theadvective acceleration component is obtained by interpolation.

The flow velocity component in a direction different from the directionof the beam is obtained from both the thus-obtained advectiveacceleration component and the stored Doppler velocity distribution.

DISCLOSURE OF INVENTION

However, even in the above-described velocity distribution measuringapparatus adopting a Doppler method using an advective accelerationvelocity, the arithmetic operation is complicated as in the othersystems, and it is impossible to solve the problem of the increase inthe size of the apparatus and a long measuring time.

Accordingly, it is an object of the present invention to eliminate theabove-described problems in the prior art and to provide an improvedvelocity distribution measuring apparatus adopting a Doppler methodwhich is capable of obtaining a velocity component in a directiondifferent from the direction of a beam by a simple arithmetic operationand at a high speed.

To achieve this aim, the present invention is characterized in thatafter the Doppler velocity in the direction of an ultrasonic orelectromagnetic beam is obtained by the transmitted and received wavesof the beam, a component in a direction different from the direction ofthe beam is obtained from the Doppler velocity data through anintegration step and a differentiation step which is obtained along thetransverse section being observed.

More specifically, the Doppler velocity distribution obtained astwo-dimensional information is first stored in a first memory. Thestored Doppler velocity data are then sequentially read out in adirection different from the direction of the ultrasonic wave, thedirection orthogonal thereto, in an ordinary case, accumulated in thedirection of readout, and the contents of the data are stored in asecond memory for the respective pixels.

In the present invention, the value obtained from accumulation, namely,the accumulated value at each pixel in the direction in which the dataare read out coincides a value known as a stream function, as will beobvious from the later explanation.

In the present invention, all the stream functions are further storedtwo-dimensionally along the transverse section and then differentiatedin the direction of the beam.

The present inventors have found that the thus-differentiated value ofeach pixel constitutes a velocity component in a direction differentfrom the direction of the beam, for example, the direction orthogonalthereto and is useful for the measurement of the flow velocitydistribution, as is clear from the following detailed explanation.

The Doppler velocity often has a three-dimensional expanse in the actualobject being examined. In this case, since the cumulatively integratedDoppler velocity has a component in the direction vertical to the beamscanning plane, compensating calculation is preferably executed when astream function is obtained in order to compensate this component. Thepresent invention enables further accurate velocity distributionmeasurement by the compensating calculation.

According to the present invention, the thus-measured two-dimensionalcomponents enable the calculation of the velocity distribution along apredetermined transverse section being observed, the accelerationdistribution and the pressure in the closed region, etc.

According to the present invention, the Doppler velocities of a fluid inthe direction of an ultrasonic or electromagnetic beam is obtained fromthe beam which is used for linear or sector scanning in the same way asin the prior art, and the thus-obtained Doppler velocities are stored ina first memory.

The Doppler velocities are then read out in a direction different fromthe direction of the beam, and the cumulatively integrated value at eachpixel is obtained by cumulative integration of the Doppler velocities inthe direction of readout, and is stored in a second memory as acumulatively integrated value distribution.

The cumulatively integrated value distribution represents the streamfunction in the fluid.

According to the present invention, the stream functions are againsequentially differentiated in the direction of the ultrasonic beam andare stored in a third memory as a differential value distribution, whichrepresents a Doppler velocity component in the direction of readout.

Consequently, it is possible to measure the true Doppler velocity ateach pixel from the component in the direction of the beam stored in thefirst memory and the component in the direction of readout stored in thethird memory. The Doppler vector is visually displayed on atwo-dimensional colored screen or the like, and it is possible to knowthe acceleration distribution and the pressure distribution in theclosed region, if necessary.

It goes without saying that the results of observation in accordancewith the present invention are utilized for not only the observation ofa distribution in the form of an image display but also for variousanalyses in the form of numerical information.

According to the present invention, it is also preferable to use notonly the observed Doppler velocity component in the direction of thebeam but also the data obtained by inferring and removing the componentin the direction orthogonal to the scanning plane from the Dopplervelocity component. Such compensating calculation is possible fromvarious data on the object being examined. For example, in the case ofobserving a bloodstream in the heart, the compensation is obtained fromthe calculation of the model conditions inferred from the pressure ateach part of the heart, the shape of the heart, etc.

Brief Description of Drawings

FIG. 1 is an explanatory view of a stream function in the flow field towhich the present invention is applied;

FIG. 2 is an explanatory view of the relationship between the measuredvalue and the stream function obtained from the linear scanning of anobject being examined with an ultrasonic beam which is transmitted toand received from the object;

FIG. 3 is an explanatory view of a stream function in the polarcoordinates in the case of applying the present invention to the sectorscanning in an ultrasonic diagnostic apparatus;

FIG. 4 is a block circuit diagram of a preferred embodiment of a Dopplervelocity measuring apparatus according to the present invention which isapplied to a sector scanning ultrasonic diagnostic apparatus;

FIGS. 5 to 9 are explanatory views of the state in which the bloodstreamdistribution in the heart shown in FIG. 4 is measured;

FIGS. 10 and 11 are explanatory views of the principle of measurement inthe present invention in a three-dimensional stream; and

FIGS. 12 and 13 are block diagrams of the main parts of preferredembodiments of the present invention in a three-dimensional stream.

Best Mode for Carrying Out the Invention

Preferred embodiments of the present invention will be explainedhereinunder with reference to the accompanying drawings.

Principle of Invention

The equation of motion with respect to a general flow will first beexplained with reference to FIG. 1.

In order to visibly catch the flow field at a certain moment, astreamline is utilized. Generally, when the directions of all tangentsto a curve in a flow field agree with the direction of a streamlinevector with respect to the curve at every point on the curve, this curveis called a streamline, which is represented by the reference numeral 1in FIG. 1.

For example, when a large amount of aluminum powder dispersed on thesurface of a closed channel stream is photographed with a slow shutterspeed, the movement of the aluminum powder comes out as short lines onthe film and a multiplicity of lines connecting those short lines comeout as the streamlines 1 shown in FIG. 1. Although the streamline 1 istemporally constant in a steady flow, the shape of the streamline 1changes at every moment in an unsteady flow, so that it is possible tovisually observe the flow in a predetermined region by seeing the changeof the streamline.

It is possible to analyze the flow field by the equation of motion onthe basis of the streamline, and a function important for this analysisis known as a stream function.

That is, when a certain function S (x, y) has the followingrelationship, this function is called a stream function: ##EQU1## Thestream function represented by the equation (1) is a stream function ina two-dimensional stream. In the present invention, the flow can besufficiently measured by such two-dimensional analysis. It goes withoutsaying that processing of a three-dimensional stream enables moreaccurate measurement in the actual measurement of bloodstream or thelike, and this will be described later.

The symbols u and v represent the velocity component in the direction ofa beam and the velocity component in the direction orthogonal thereto,respectively, in a two-dimensional stream measured by a pulse-Dopplermethod.

The direction of a beam is a direction of the y-axis with the directionof the x-axis orthogonal thereto. The fundamental principle of thepresent invention is to obtain the unknown component v.

The relationship between the stream function S (x, y) and the streamlinewill be explained in the following by using the components u and v.

When the stream function S (x, y) is constant, if the function istotally differentiated, the following equation holds: ##EQU2## Thisrelationship satisfies the continuous equation in two dimensions.

When the relationship represented by the equation (1) is substitutedinto the equation (2), the following equation holds:

    -vdx+udy=0                                                 . . . (3)

That is, ##EQU3## This means that the direction sx/dy of a tangent to aline in which S (x,y) is constant agrees with the direction of thestreamline 1 shown in FIG. 1 in which the x component is u and the ycomponent is v.

In other words, it is evident that the locus of points in which thestream function is constant is a streamline and that the relationshipsrepresented by the equations (1) to (4) constantly hold in atwo-dimensional stream.

From the above analysis it is clear that since the Doppler velocityobtained by an ultrasonic pulse-Doppler method is a velocity component uin the direction of the x-axis, it is possible to obtain the streamfunction S (x, y) by integrating the Doppler velocity component u in thedirection of the y-axis which is orthogonal to the direction of the beam(x-axis) from the right-hand term in the equation (1).

It is also evident that if the thus-obtained stream function S (x, y) isthen differentiated again in the direction of the x-axis, which is thedirection of the beam, the x component v in the direction orthogonal tothe x-axis is obtained from the equation (1).

FIG. 2 schematically shows the Doppler velocity detecting operation of aDoppler velocity measuring apparatus according to the present invention.

In FIG. 2, when an ultrasonic probe 2 transmits an ultrasonic beam 4 toa fluid, for example, an object 3 being examined and the reflected echois detected, the Doppler velocity data u in the direction of theultrasonic beam 4 in the fluid 3 is obtained from a change in thefrequency. It will be understood that if it is assumed that thedirection of the beam is the x-axis, the direction agrees with thedirection in the flow field shown in FIG. 1.

Actually, the probe 2 scans in the direction orthogonal to the directionof the beam x, namely, in the direction of the y-axis, and the Dopplervelocity u, which is a component obtained by the ultrasonic beam 4 isdata at each pixel on a two-dimensional transverse section.

It will therefore be understood that the velocity data v in thedirection orthogonal to the ultrasonic beam 4 can be obtained as thevelocity data v in the orthogonal direction from the direction of thetangent to the streamline 1 shown in FIG. 1 and the Doppler velocitydata u by obtaining the stream function S of the streamline 1 shown inFIG. 1.

The equation (1) already defines: ##EQU4## When the equation (5) isintegrated with respect to y, ##EQU5## and the stream function (x, y) isobtained.

It is therefore possible to obtain the streamline 1 shown in FIG. 1 bydisplaying the data on the predetermined values of the stream function S(x, y), thereby detecting the velocity data v in the directionorthogonal to the ultrasonic beam 4 in the above-described way.

In the present invention, in the actual operation process of theequations (5) and (6), the cumulative integration represented by theequation (6) is carried out in the direction of the y-axis. Since thecomponent u, namely, the Doppler velocity has already been obtained,mere cumulative integration of this component in the y-axis, which isorthogonal to the direction x of the beam produces the accumulated valueat each pixel, namely, the stream function. By differentiating thestream function obtained at each pixel again in the direction of thebeam, namely, in the direction of the x-axis, the component v in theorthogonal direction, namely, in the direction of y is obtained.

As described above, it will be understood that if only a two-dimensionalflow field is considered in FIG. 2, it is possible to obtain thecomponent v by first obtaining the stream function of thetwo-dimensional field by cumulatively integrating the component u, whichis the Doppler velocity, in a direction different from the direction ofthe component u and then differentiating the stream function in thedirection of the beam, namely, along the x-axis.

The principle of obtaining a component in a direction different from theultrasonic beam from the Doppler velocity distribution in the directionof the ultrasonic beam is as described above. It will be understood thatsuch two dimensions are obtained as two-dimensional data in thedirection of an ultrasonic beam and the direction orthogonal thereto bya linear scanning of an ultrasonic probe by linear scanning and as thecomponents in the direction of the ultrasonic beam and the direction incontact therewith by electronic sector scanning. Thus, desired velocitymeasurement is enabled both in linear and sector scanning.

Stream Function in Polar Coordinates

In FIG. 2, the ultrasonic probe 2 mechanically or electronically andlinearly scans in the direction of the y-axis and, as a result, the flowfield is represented by the x,y rectangular coordinates. In the presentinvention, it is naturally possible to execute the analysis using thestream function in polar coordinates.

Especially in the case of observing the bloodstream in the heart, thesector scanning of an ultrasonic beam is often utilized. In order toanalyze the Doppler velocity obtained by such sector scanning, it isconvenient to represent the Doppler velocity in polar coordinates withthe position of the ultrasonic probe as the origin, as shown in FIG. 3.

In FIG. 3, polar coordinates are supposed to have the beam transmittingpoint of a vibrator 12 as the origin. In the polar coordinates, it isassumed that the stream function of a two-dimensional stream is S (r,θ), the velocity components at the point (r, θ) are (u, v), and thefollowing relationship holds: ##EQU6##

This relationship is the same as that represented by the equation (1) inthe rectangular coordinates, and satisfies the continuous equation intwo dimensions. That is, ##EQU7##

If the equation (9) is totally differentiated on the assumption that S(x, y) is constant, ##EQU8## This equation indicates that the lineconnecting the points of the stream function at the same level is astreamline.

The stream function is obtained by integrating the equation (8) and isrepresented by the following equation:

    S(r, θ)=r∫udθ                             . . . (11)

In this way, it is also possible to obtain a component in a directiondifferent from the direction of the ultrasonic beam from the Dopplervelocity obtained by sector scanning by the analysis of polarcoordinates in a similar processing to that of the rectangularcoordinates.

More specifically, the Doppler velocity signal obtained by sectorscanning only contains the component in the direction of the ultrasonicbeam. This component for one frame on the transverse section is firststored in the memory.

The Doppler velocities at the respective points are read out in adirection different from the direction of the beam, namely, in thedirection of a readout line along the arc which is equidistant from thebeam origin by r, and are cumulatively integrated.

As a result, the cumulatively integrated value represents the streamfunction in the same way as in the case of the rectangular coordinates,as is clear from the equation (11).

The stream function distribution is differentiated again in thedirection of the beam, thereby enabling the component along the arcwhich is equidistant from the beam origin to be obtained.

Example of Sector Scanning

It is obvious from the above explanation that the present invention isapplicable to both linear scanning and sector scanning An embodiment ofthe present invention which is applied to an ultrasonic diagnosticapparatus will be explained with reference to the example shown in FIG.4.

In FIG. 4, an ultrasonic probe 22 is brought into close contact with thesurface of an object 23 being examined. In this embodiment, thebloodstream distribution in the heart is observed. The probe 22 in thisembodiment is composed of an electronic sector probe and transmits asector beam 24 to the heart in accordance with an oscillation signalfrom a sector scanning circuit 25, as shown in FIG. 4.

As is well known, the pulse burst frequency of the ultrasonic beam iscontrolled by the oscillation signal obtained from an oscillator 26.

The output of the oscillator 26 is further supplied to a controller 27to provide the controller 27 with a synchronous clock signal forcontrolling the entire ultrasonic diagnostic apparatus.

The controller 27 therefore drives the sector scanning circuit 25 inaccordance with the control signal and controls the probe 22 so as totransmit the sector ultrasonic beam at a predetermined timing and toelectronically scan a predetermined sector range with the beam.

The echo reflected from each part of the heart, which is the objectbeing examined, is electrically received by the probe 22 and istransmitted from the sector scanning circuit 25 to the receiving circuit28. The receiving circuit 28 determines the direction of reception inaccordance with the transmitted beam 24, and separates the receivedsignals depending upon the frequency so as to take out only the signalsnecessary for Doppler deviation. As is well known, the receiving circuit28 is provided with at least a high pass filter for the above-describedselection, and removes the signals from the heart wall and other tissueswhich slowly change while selectively taking out the signals from thebloodstream which quickly changes, thereby enabling the removal of thesignals having a large intensity from the heart wall.

The thus-received signals are supplied to a pulse-Doppler detector 29and detected after they are mixed with the transmitting frequencysuppled from the sector scanning circuit 25. The pulse-Doppler detector29 outputs a Doppler displacement signal, namely, Doppler velocity.

The detected Doppler velocities are converted into digital signals by anA/D converter 30 and sequentially stored in a first memory 31. In thisembodiment, the first memory 31 is composed of a two-dimensional memorysuch as an image frame memory, and has a capacity for storing at leastone sector scanning frame. The writing operation of the first memory 31is controlled by an address control signal output from a write addresscontroller 32 which is synchronously controlled by the sector scanningcircuit 25. Data is written at a pixel corresponding to the depth (r) ofthe reflected echo and the scanning angle (θ).

In this way, the bloodstream velocity component u in the direction ofthe ultrasonic beam 24 for one scanning frame is stored in the firstmemory 31, and by using the component u, the component v is calculatedin accordance with the present invention.

In the present invention, if the first memory has a capacity for atleast three scanning frames, while the component v is calculated, thenext sector scanning is executed, which is stored in a vacant memory,thereby enabling signal processing at real time by alternately storingthe component u and reading the component u for the calculation of thecomponent v.

The contents of the first memory 31 are sequentially read out along thearc having the same radius r, as is obvious from the above explanation,and are cumulatively integrated by the integrator 32.

The reading operation of the first memory 31 is preferably so controlledby a read address controller 33 as to be executed in accordance with theinstruction from the controller 27 and in association with the scanningof the next frame by the sector scanning circuit 25.

The integrator 32 sequentially cumulatively integrates the input dataand supplies the integrated values to a second memory 34 composed of animage frame memory so as to store the integrated values at predeterminedpositions. The writing operation of the second memory 34 is controlledby a write address controller 35 synchronously with the read addresscontroller 33 which controls the reading operation from the first memory31 in the direction of readout along the arc.

In this way, the distribution of the stream function S (r, θ) at eachpoint of the scanning plane of the transverse section is stored in thesecond memory 34.

FIG. 5 shows the displayed image of the Doppler velocity distributionstored in the first memory 31. As is obvious from FIG. 5, the Dopplervelocity is represented by light and shade. The velocity increases withthe degree to which the shade becomes darker.

The image shown in FIG. 5 is a conventional image of Doppler bloodstreamdistribution. Since the component in the direction of the ultrasonicbeam solely is taken into consideration in this image, as describedabove, a great deal of skill is required for inferring the actualbloodstream.

The present invention is characterized in that the integrator 32cumulatively integrates the Doppler velocity shown in FIG. 5 in thedirection of readout along the arc. The reference numeral 100 in FIG. 6represents one readout line and the cumulatively integrated values alongthe readout line 100 are represented by the curve 101.

As is clear from the above explanation, the curve 101 is the streamfunction S (r, θ), and the result of the cumulative integration of thestream function S (r, θ) over the entire scanning region is shown as adisplayed image in FIG. 7.

As is clear from FIG. 7, the image distinctly shows the direction offlow of the bloodstream in the heart. The image shown in FIG. 7 isobtained by processing the data in the second memory 34 by an imageprocessor 36, as shown in FIG. 4. The data in the second memory 34 issupplied to the image processor 36 by the read address controller 37under the control of the controller 27.

The image processor 36 normalizes the stream function data and convertsthe data into analog data which are supplied from a switch 38 to a CRT40 for display through a display controller 39 as color image signals.

The switch 38 changes over between the stream function display and theflow vector diagram and is composed of contact devices manually orautomatically switched.

The display controller 39 includes a color display circuit in thisembodiment, and is capable of displaying the stream functions as amultiple-color image at real time.

The stream function S (r, θ) is read out of the second memory 34, asdescribed above, and sequentially differentiated by a differentiator 41.The differentiating operation is carried out in order to obtain thecomponent v in the direction of the arc. For this purpose, the readaddress controller 37 so controls that the contents of the second memory34 are again read out in the direction of the beam, and thedifferentiation operation is sequentially carried out in the directionof readout.

FIG. 8 shows the differentiating operation. A plurality of streamfunctions 110 to 113 shown in FIG. 8 are sequentially differentiated inthe direction of the beam 24 so as to obtain the arc components v, whichare sequentially stored in a third memory 42.

The storing operation of the third memory 42 is controlled by a writeaddress controller 43. In this embodiment, since the writing operationis controlled in association with the data reading operation of thesecond memory 34, a synchronous signal C₃ is supplied from the readaddress controller 37 to the input of the write address controller 43.

When the arc components v for one frame are stored in the third memory42, the arc components v and the components u in the direction of thebeam stored in the first memory 31 are supplied to an image processor 44and converted into predetermined image signals.

These signals are supplied to the display controller 39 through theswitch 38, and are displayed as a flow vector diagram, for example, asthe image of a synthesized vector of the components u and v, as shown inFIG. 9 in the same way as in the case of displaying the streamfunctions.

Thus, according to the present invention, it is possible to obtain acomponent in a direction different from the beam axis which isimpossible in the prior art, thereby enabling the velocity measurementwith high accuracy.

Stream function of three-dimensional stream

In the above explanation, it is assumed that the stream being observedis a two-dimensional stream, but in most cases, an object of measurementis a three-dimensional stream, as described above simply. For example,the bloodstream in the heart exhibits complicated three-dimensionalmotion.

The continuous equation in three dimensions is represented by thefollowing equation: ##EQU9## The component w which is orthogonal to theplane scanned with an ultrasonic beam is included, and due to theinfluence of this component, an error still remains in the analysis of atwo-dimensional stream.

Actually, processing a flow as a two-dimensional stream results insufficient signal processing, but in the following embodiment, theorthogonal component w is further compensated.

The improvement according to the present invention in which thecomponent w is inferred from another component such as the component uwill be described in the following.

The principle of the improvement is based on the following standpoint.For example, a component u on the transverse section is a quantity whichfundamentally three-dimensionally diverges, so that the component u hasa divergent component on not only the x-y plane but also the x-z plane.If a divergent component, for example, u₂ an unknown component w cancelout each other, it is possible to remove the unknown component w by aresidual component u₁ which is obtained by subtracting the x-z planecomponent u₂ from the measured component u.

FIG. 10 shows the component u observed at the point O of x, y, zthree-dimensional coordinates. Since the component u divergesthree-dimensionally, as described above, this can be represented by thex-y plane and the x-z plane. In FIG. 10, only the x-y plane is analyzedto simplify explanation.

It is naturally considered that a stream constantly returns like avortex. The measured component u draws a vortex on the x-y plane as thecomponent u₁ which is obtained by subtracting the component u₂ forcancelling out the later-described component w from the measuredcomponent u. In FIG. 10, the u component forms a return vortex u₁₊ onthe positive side of the x-y plane and a return vortex u₁₋ on thenegative side of the x-y plane.

Therefore, the component u₁ is represented as follows:

    u.sub.1 =(u.sub.1+)+(u.sub.1-)

Similarly, FIG. 11 shows the component u₂ on the x-z plane whichdiverges at the point O. The component u₂ is similarly represented asfollows:

    u.sub.2 =(u.sub.2+)+(u.sub.1-)

What is important in the principle of this embodiment is that it isconsidered that the flow velocity component u₂ on the x-z plane of afluid which flows into the point O agrees with the velocity component inthe direction of w. Therefore, if the component u₂ is removed, it ispossible to remove the error due to the component w without measuringthe velocity in the direction of w.

It will therefore be understood that the equation (12) is represented bythe following equation. ##EQU10## In the equation (13), since thecomponent u₂ and the component w cancel out each other, if u₂ isdetermined so that the following equation holds: ##EQU11## thecontinuous equation in three dimensions is represented by the followingequation: ##EQU12## Thus, it will be understood that the flow can alsobe processed by the equation for a two-dimensional stream in thisembodiment.

In this embodiment, only the Doppler velocity component distribution u₁is cumulatively integrated after the component u₂ which corresponds tothe component w obtained from the received signal by the probe, namely,the component u with the known conditions, for example, in the case ofthe measurement of the bloodstream in the heart, the size of the heart,the position of a valve, the blood pressure, etc. taken intoconsideration is subtracted from the measured value u.

FIG. 12 shows an example of cumulative integration in athree-dimensional stream in accordance with the present invention. Thecumulative integration shown in FIG. 12 is characterized in that whenthe Doppler velocity information stored in the first memory 31 is readout in a direction different from the direction of the beam, theinformation is supplied to the integrator 32 through a three-dimensionalcompensation circuit 50.

The Doppler velocity data u stored in the first memory and read out in adirection different from the direction of the beam, for example, thedirection orthogonal thereto contains the component w in the directionof the z-axis, as described above. This component is the component u₂.The three-dimensional compensation circuit 50 is fundamentally composedof a low pass filter so as to remove the component u₂.

As is clear from FIG. 11, the direction in which the memory data forcumulative integration are read out is the direction of the y-axis, andthe component u₂ for cancelling out the component w in the direction ofthe y-axis exists on the x-z plane. As a result, most of the spatialfrequency components read out in the direction of the y-axis belong to ahigh-frequency region.

Therefore, the components u₂ to be removed are only high-frequencycomponents in the data on principle, so that provision of a low passfilter at the precedent step to the integrator 32 enables the componentu₂ to be removed to a substantially practical level. It is thereforepossible to take out only the compensated component u₁ from thethree-dimensional compensation circuit 50 composed of a low pass filterand, as a result, the cumulative integration is carried out with respectto the effective component u₁ solely with the error removed therefrom.Thus, highly accurate measurement is enabled with respect to athree-dimensional fluid.

In the present invention, the three-dimensional compensation circuit 50is not restricted to a mere low pass filter. More complete eliminationis enabled by discriminating between a plurality of spatial frequencycomponents of the data read out of the first memory 31 in the orthogonaldirection, connecting the outputs of discrimination to the correspondinglow pass filters, and synthesizing the outputs obtained from theplurality of low pass filters.

That is, in the single low pass filter shown in FIG. 12, it is assumedthat the component u₂ to be removed in FIG. 11 is a single returnvortex. Actually, a plurality of return vortices exist on the x-z plane,and the sizes of these vortices are preferably discriminated so as toprocess the vortices separately from each other depending upon the size.

FIG. 13 shows such frequency processing circuits arranged in parallel.The data read out of the first memory 31 are first classified dependingupon predetermined spatial frequencies by the frequency discriminator 51of the three-dimensional compensation circuit 50. In this embodiment,three frequency bands are discriminated, and low pass filters 52, 53 and54 having different cut-off frequencies are arranged in parallel incorrespondence with the respective frequency bands.

It goes without saying that the number of low pass filters and thenumber of frequencies discriminated may be selected as desired.

According to this embodiment, it is possible to process the returnvortices from a small vortex to a large vortex on the x-z plane shown inFIG. 11 separately from each other and the optimum three-dimensionalcompensation of the spatial distribution of the components u₂ isenabled.

The three-dimensional compensation circuit 50 in FIG. 13 includes asynthesizer 55 for synthesizing the outputs of the low pass filters 52,53 and 54, whereby it is possible to supply only the component u₁ withthe component w removed to the integrator 32 for cumulative integration.

In the embodiments shown in FIGS. 12 and 13, only the integrator 32shown in FIG. 4 is improved and the other structure is the same as thatshown in FIG. 4, so that the total circuit structure is omitted.

As is clear from the above explanation, use of such Doppler velocitiesprocessed in advance enables the influence of the component w to beremoved and velocity information containing very few error to beobtained in the same technique shown in the first embodiment.

The present invention having the above-described structure enables themeasurement of the velocity of a flow by a Doppler method with easinessand at a low cost. It is possible to display the stream function and thestreamline at real time from the thus-obtained velocity information,whereby it is possible to obtain a desired velocity distribution and thepressure distribution or the like in the closed region obtained from thevelocity distribution.

What is claimed is:
 1. A Doppler flow velocity measuring apparatus,comprising:a means for obtaining a Doppler velocity distribution in thedirection of a beam by utilizing a Doppler effect obtained from the echoreflected from a fluid when an ultrasonic wave or an electromagneticwave is transmitted to and received from said fluid and scanning adesired transverse section with reflected echo; a first memory means forstoring the Doppler velocity distribution; a means for obtaining astream function by reading out the stored Doppler velocity in adirection orthogonal to the direction of said beam and cumulativelyintegrating said Doppler velocity at each point; a second memory meansfor two-dimensionally storing said stream function obtained; and a meansfor obtaining the velocity component in the scanning plane which isorthogonal to the direction of said beam by reading out the streamfunction distribution in the direction of said beam and differentiatingsaid stream function distribution in the direction of said beam.
 2. ADoppler flow velocity measuring apparatus according to claim 1, whereinsaid direction in which said Doppler velocity is cumulatively integratedis the direction orthogonal to the direction of said beam.
 3. A Dopplerflow velocity measuring apparatus according to claim 1, wherein saidDoppler velocity obtained from said reflected echo is the data subjectedto compensation operation so as to remove the component in the directionorthogonal to said transverse section.
 4. A Doppler flow velocitymeasuring apparatus according to claim 3, wherein said compensationoperation includes a means for reading out Doppler velocity data in adirection different from the direction of said beam and cumulativelyintegrating said Doppler velocity data at each point, and a low passfilter for removing the high-frequency component of said data read outbefore the cumulative integration.